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Math Help - orbit

  1. #1
    Senior Member Sampras's Avatar
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    orbit

    Suppose  f,g \in X and have the same pattern. Prove that  W(f) = W(g) .

    Now an orbit of and element  f in  X is all the "possible stuff" that a permutation  \pi can map  f to. So does  f,g \in X imply that they are in the same orbit?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Sampras View Post
    Suppose  f,g \in X and have the same pattern. Prove that  W(f) = W(g) .

    Now an orbit of and element  f in  X is all the "possible stuff" that a permutation  \pi can map  f to. So does  f,g \in X imply that they are in the same orbit?
    I'm sorry. Maybe some other member will swoop in and help you. But if not, I just have two questions. What does 'pattern' mean in this context? and what is W(y) represent. Also, what is X? Just some group under consideration? If so, then f,g\in X does not mean that f\in\mathcal{O}(g) or vice versa (which is really the same thing).
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  3. #3
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    Quote Originally Posted by Sampras View Post
    Suppose  f,g \in X and have the same pattern. Prove that  W(f) = W(g) .

    Now an orbit of and element  f in  X is all the "possible stuff" that a permutation  \pi can map  f to. So does  f,g \in X imply that they are in the same orbit?

    If you don't properly define your "stuff" people won't properly understand it: what are f,g? What is a "pattern" for them? What is W(f)? What is X?
    What action of what group (presumably S_n) on what set are we talkin about here?

    Tonio
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